Let each different arrangement of all the letters of DELETED

Question

Let each different arrangement of all the letters of DELETED be called a word.
(a) How many words are possible?
(b) In how many of these words will the D's be separated?

duttsit · Answer

(a) total words = 7! / 3! * 2! as there are 3 Es and 2 Ds
 = 420

(b) total number of words where both Ds are TOGETHER - count 2 Ds as 1:
 number of words = 6!/3! = 120
 number of words where Ds are not together = 420 - 120 = 300

chriswil2005 · Answer

A. 7!/(3!2!). 7=total amount of letters, must divide repeated elements. 3=total number of repeating letter E. 2= amount of repeating letter D


B. I will try (the amount above)-(the amount of ways in which D will not be separated). I basically take DD as one letter. However, I do not know how to set it up. Help anyone?

ywilfred · Answer

(A) 7!/3!2! (Divide by 3! as we have 3 E's and 2! as we had 2 D's)-> 420

(B) Treat the 2 D's as one entity, then we will have 6!/3! = 120 words where the two D's are together. So # of words where D are aparts = 420-120 = 300

gsr · Answer

OA is 420 and 300. I am weak in this area. Can someone explain more in detail how we get the 6! in (b)? I am just not able to visualize :cry:

Also, Titelist, do you hear me?!!! Need some 'graphical' help!!

HIMALAYA · Answer

total possiblities = 7!/(3! 2!) = 420 total possibilities with D's togather = 6(5!)/3! = 6!/3! = 120 so poss D's seperate = 420 - 120 = 300 in the following ways, we can arrange D's togather so that we get 120: 1st place = DD----- = 2(5!/3!2!) = 5!/3! = 20 2nd place = -DD---- = 5!/3! = 20 3rd place = --DD--- = 5!/3! = 20 4th place = ---DD-- = 5!/3! = 20 5th place = ----DD- = 5!/3! = 20 6th place = -----DD = 5!/3! = 20 total = 120 i am not sure whether it helps or not... 8-)

gsr · Answer

6(5!) /3! - This was the missing link!!! Thanks Himalaya!! -------------- :wall

Left side - 'me' Right side - 'probability'

ywilfred · Answer

There are 7 letters, but because we treated the two D's as one entity, it becomes 6 letters now. (We treat D as an entity to calculate number of words where the two D's will be together). Since we now have 6 spaces to fill, so it becomes 6!

HIMALAYA · Answer

precisely the above expression is =  2 (6)(5!)/(3! 2! ) = 6!/3! = 120

Let each different arrangement of all the letters of DELETED

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